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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="mesfunc5.html#NM1">ExtREAL_sequence</a>;<br/>

<b>assume </b><a NAME="E1:87"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V3" target="_self">without-infty</a>
 ;<br/>

<a NAME="E2:87"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E3:87"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K17">rng</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="supinf_1.html#K2">-infty</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> 1 )
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E1:87"><i><font color="Green">E82</font></i></a>, <a class="ref" href="mesfunc5.html#D5" target="_self">Def5</a>, <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E4:87"/><b>then </b>
 <a href="supinf_1.html#K2">-infty</a>  is  not    <a href="supinf_1.html#M1">majorant</a> of  <a href="supinf_2.html#K17">rng</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="supinf_1.html#D9">SUPINF_1:def 9</a></i>;<br/>
<a NAME="E5:87"/><b>then </b>
 <a href="supinf_1.html#K6">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K17">rng</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a> 
 
<b>by </b><i><a class="ref" href="supinf_1.html#D16">SUPINF_1:def 16</a></i>;<br/>
<b>hence </b><a NAME="E6:87"/>
(  <a href="supinf_1.html#K6">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K17">rng</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a>  or  <a href="supinf_1.html#K6">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K17">rng</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K1">+infty</a>  )
 <b>by </b><i><a class="ref" href="xxreal_0.html#T14">XXREAL_0:14</a></i>;<br/>


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